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looks like a stipple finish paint to me ,on a substrate that may well be an asbestos product .
It's better but not necessarily easier- replacing the plasterboard will require that you take down the old plaster (or whatever it is) and replace the cornice and skirting (assuming there are no doors or windows in this particular wall- if there is you are up for architrave too). If you're lucky you can re-use the existing ones if you take care in removal. Putting new plasterboard over the top of the existing plasterboard is annoying as you also need to re-do the cornice and skirting.
Why do you think the wall may be asbestos? Is the rest of the house asbestos lined? What room of the house is the wall in? Can you scrape back some of the textured paint finish and have a look at what is underneath?